Eddy Plate Working Princpal Semi Balance Rudder
from which Figure 8.7 is plotted.
In 1957 the International Towing Tank Conference (ITTC)5 adopted a model-ship correlation line, based on:
Rf 0.075
The term correlation line was used deliberately in recognition of the fact that the extrapolation from model to full scale is not governed solely by the variation in skin friction. Q values from Schoenherr and the ITTC line are compared in Figure 8.8 and Table 8.2.
0.010 0.008
0.006
0.001
I.T.T.C.1 |
957 | ||||||||||||||||||||||||||||
Schoenhw | |||||||||||||||||||||||||||||
Reynolds' number, Reynolds' number, Figure 8.8 Comparison of Schoenherr and ITTC 1957 lines Table 8.2 Comparison of coefficients from Schoenherr and ITTC formulae Reynolds'number Schoenherr ITTC 1957 10(i 0.00441 0.004688 107 0.00293 0.003000 10® 0.00207 0.002083 109 0.00153 0.001531 Eddy making resistance or viscous pressure resistance fn a non-viscous fluid the lines of flow past a body close in behind it creating pressures which balance out those acting on the forward part of the body. With viscosity, this does not happen completely and the pressure forces on the after body are less than those on the fore body. Also where there are rapid changes of section the flow breaks away froin the hull and eddies are created. The effects can be minimized by streamlining the body shape so that changes of section are more gradual. However, a typical ship has many features which are likely to generate eddies. Transom sterns and stern frames are examples. Other eddy creators can be appendages such as the bilge keels, rudders and so on. Bilge keels are aligned with the smooth water flow lines, as determined in a circulating water channel, to minimize the effect. At other loadings and when the ship is in waves the bilge keels are likely to create eddies. Similarly rudders are made .is streamlined as possible and breakdown of flow around them is delayed by this means until they are put over to fairly large angles. In multi-shaft ships the shaft bracket arms are produced with streamlined sections and are aligned with the local flow. This is important not only for resistance but to improve the flow of water into the propellers. Flow break away can occur on an apparently well rounded form. This is due to the velocity and pressure distribution in the boundary laser. The velocity increases where the pressure decreases and vice versa. Bearing in mind that the water is already moving slowly close into the huli, the pressure increase towards the stern can bring the water to a standstill or even cause a reverse flow to occur. That is the water begins to move ahead relative to the ship. Under these conditions separation occurs. The effect is more pronounced with steep pressure gradients which are associated with full forms. Appendage resistanceAppendages include rudders, bilge keels, shaft brackets and bossings, and stabilizers. Each appendage has its own characteristic length and therefore, if attached to the model, would be running at an effective Reynolds' number different from that of the main model. Thus, although obeying the same scaling laws, its resistance would scale differently to the full scale. That is why resistance models are run naked. This means that some allowance must be made for the resistance of appendages to give the total ship resistance. The allowances can be obtained by testing appendages separately and scaling to the ship. Fortunately the overall additions are generally relatively small, say 10 to 15 per cent of the hull resistance, and errors in their assessment are not likely to be critical. Wind resistanceIn conditions of no natural wind the air resistance is likely to be small in relation to the water resistance. When a wind is blowing the fore and aft resistance force will depend upon its direction and speed. If coming from directly ahead the relative velocity will be the sum of wind and ship speed. The resistance force will be proportional to the square of this relative velocity. Work at the National Physical Laboratory6 introduced the concept of an ahead resistance coefficient (ARC) defined by: fore and aft component of wind resistance ipViUT where VR is the relative velocity and Ar is the transverse cross section area. For a tanker, the ARC values ranged from 0.7 in the light condition to 0.85 in the loaded condition and were sensibly steady for winds from ahead and up to 50° off the bow. For winds astern and up to 40° off the stern the values were -0.6 to -0.7. Between 50° off the bow and 40° off the stern the ARC values varied approximately linearly. Two cargo ships showed similar trends but the ARC values were about 0.1 less. The figures allowed for the wind's velocity gradient with height. Because of this ARC values for small ships would be relatively greater and if the velocity was only due to ship speed they would also be greater. Data is also available7 for wind forces on moored ships. CALCULATION OF RESISTANCEHaving discussed the general nature of the resistance forces a ship experiences and the various formulations for frictional resistance it is necessary to apply this knowledge to derive the resistance of a ship. The model, or data obtained from model experiments, is still the principal method used. The principle followed is that stated by Froude. That is, the ship resistance can be obtained from that of the model by: (1) measuring the total model resistance by running it at the corresponding Froude number; (2) calculating the frictional resistance of the model and subtracting this from the total leaving the residuary resistance; (3) scaling the model residuary resistance to the full scale by multiplying by the ratio of the ship to model displacements; (4) adding a frictional resistance for the ship calculated on die basis of the resistance of a flat plate of equivalent surface area and roughness; (5) calculating, or measuring separately, the resistance of appendages; (6) making an allowance, if necessary, for air resistance. ITTC methodThe resistance coefficient is taken as C= (Resistance)/\p5V2. Subscripts t, v, r and f for the total, viscous, residual and frictional resistance components. Using subscripts m and s for the model and ship, the following relationships are assumed: ^is = Qm = Qm — Qm c;.s = (i + k)Qs + dCp where (5Cp is a roughness allowance. The values of Q are obtained from the ITTC model-ship correlation line for the appropriate Reynolds' number. That is, as in Table 8.3: 0.075 k is determined from model tests at low speed and assumed to be independent of speed and scale. The roughness allowance is calculated from: X 10 where k. is the roughness of hull, i.e., 150 X 10-6m and L is the length on the waterline. The contribution of air resistance to Qs is taken as 0.001 AT/S where At is the transverse projected area of the ship above water. Table 8.3 Coefficients for the ITTC 1957 model-ship correlation line Reynolds'number Ct Reynolds'number ( t Reynolds'number Ct Reynolds'number ( t Table 8.3 Coefficients for the ITTC 1957 model-ship correlation line
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